Opt Lett. 2013 Sep 15;38(18):3514-7. doi: 10.1364/OL.38.003514.
We derive macroscopic equations of motion for the slowly varying electric field amplitude in three-dimensional active nonlinear optical nanostructures. We show that the microscopic Maxwell equations and polarization dynamics can be simplified to a macroscopic one-dimensional problem in the direction of group velocity. For a three-level active material, we derive the steady-state equations for normal mode frequency, threshold pumping, nonlinear Bloch mode amplitude, and lasing in photonic crystals. Our analytical results accurately recapture the results of exact numerical methods.
我们推导出了在三维主动非线性光学微结构中缓慢变化的电场幅度的宏观运动方程。我们表明，微观的麦克斯韦方程组和极化动力学可以简化为沿群速度方向的宏观一维问题。对于三能级激活材料，我们推导出了模频率的稳态方程、阈值泵浦、非线性布洛赫模幅度以及光子晶体中的激光。我们的分析结果准确地再现了精确数值方法的结果。
